Apparatus and method for optical raster-scanning in a micromechanical system

ABSTRACT

A method of operating a micromechanical scanning apparatus includes the steps of identifying a radius of curvature value for a micromechanical mirror and modifying a laser beam to compensate for the radius of curvature value. The identifying step includes the steps of measuring the far-field optical beam radius of a laser beam reflected from the micromechanical mirror. The measured far-field optical beam radius is then divided by a theoretical far-field optical beam radius reflected from an ideal mirror to yield a ratio value M. An analytical expression for M is curve-fitted to experimental data for M with the focal-length as a fitting parameter. The focal-length value determined by this procedure, resulting in a good fit between the analytical curve and the experimental data, is equal to half the radius of curvature of the micromechanical mirror. The micromechanical scanning apparatus is operated by controlling the oscillatory motion of a first micromechanical mirror with a first micromechanical spring and regulating the oscillatory motion of a second micromechanical mirror with a second micromechanical spring.

The development of the technology described herein was supported by NSFGrant No. EEC-96-15774 for the study of high-speed, high-resolutionmicro-optical scanners. The U.S. Government may have certain rights inthis technology.

BRIEF DESCRIPTION OF THE INVENTION

This invention relates generally to optical scanners and displays. Moreparticularly, this invention relates to an optical raster-scanningmicroelectromechanical system.

BACKGROUND OF THE INVENTION

Scanning micromirrors fabricated using surface-micromachining technologyare known in the art. As used herein, a micromirror, a microscopicdevice, a micromachined device, a micromechanical device, or amicroelectromechanical device refers to a device with a third dimensionabove a horizontal substrate that is less than approximately severalmilli-meters. Such devices are constructed using semiconductorprocessing techniques.

Scanning micromirrors have numerous advantages over traditional scanningmirrors. For example, they have smaller size, mass, and powerconsumption, and can be more readily integrated with actuators,electronics, light sources, lenses and other optical elements. Morecomplete integration simplifies packaging, reducing the manufacturingcost. These factors add motivation to the development of microfabricatedscanners. In addition to displays, high-speed, high-resolutionmicro-optical scanners have numerous additional applications inmedicine, lithography, printing, data storage and data retrieval.

U.S. Pat. No. 5,867,297 (the '297 patent) entitled “Apparatus and Methodfor Optical Scanning with an Oscillatory Microelectromechanical System”describes early seminal work in the field of oscillatory micromirrors.The contents of the '297 patent are expressly incorporated by referenceherein.

The required system tolerances in a system of the type described in the'297 patent are extremely high. For example, bending of torsional hingescauses system wobble, defined as rotation about an axis in the mirrorplane orthogonal to the primary scan axis. In a two mirror systemincluding a fast mirror and a slow mirror fast mirror wobble of lessthan 1% of the total deflection angle will cause scan lines to overlapand seriously degrade image quality. In the slow mirror, rotationalerrors known as jitter, attributable to errors in following the drivingsignal, can induce non-uniform line spacing. It would be highlydesirable to establish improved mechanical linkages to enhance mirrorperformance.

Large mirror diameters and rotational angles, facilitated by a tilt-upmirror design, are key to the resolution of a scanning system. Moving alarge mirror quickly through a large angle requires high-force actuatorsand stiff springs to achieve a high resonant frequency. Mechanically,the image resolution is limited by the number of lines that the fastmirror can scan during the refresh period of the slow mirror. Optically,the resolution is given by the size, flatness and rotational angle ofthe mirror. Increasing the mirror diameter results in higher resolutiononly if the mirror is flat, or if its curvature is optically corrected.It would be highly desirable to provide a method of characterizing andcorrecting static mirror curvature to improve the performance of anoptical raster-scanning system.

SUMMARY OF THE INVENTION

A method of operating a micromechanical scanning apparatus includes thesteps of identifying a radius of curvature value for a micromechanicalmirror and modifying a laser beam to compensate for the radius ofcurvature value. The identifying step includes the step of measuring thefar-field optical beam radius of a laser beam reflected from themicromechanical mirror. The measured far-field optical beam radius isthen divided by a theoretical far-field optical beam radius reflectedfrom an ideal mirror to yield a ratio value M. An analytical expressionfor M is curve-fitted to experimental data for M with the focal-lengthas a fitting parameter. The focal-length value determined by thisprocedure, resulting in a good fit between the analytical curve and theexperimental data, is equal to half the radius of curvature of themicromechanical mirror.

The micromechanical scanning apparatus is operated by controlling theoscillatory motion of a first micromechanical mirror with a firstmicromechanical spring and regulating the oscillatory motion of a secondmicromechanical mirror with a second micromechanical spring.

The invention provides an improved optical raster-scanningmicromechanical system. Mirror performance in the system is improvedthrough the technique of characterizing and correcting static mirrorcurvature. Improved mechanical linkages that exploit symmetry reducemirror wobble. A triangular control signal maximizes the linearity ofthe scan.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention, reference should be made tothe following detailed description taken in conjunction with theaccompanying drawings, in which:

FIG. 1 illustrates an optical raster-scanning apparatus in accordancewith an embodiment of the invention.

FIG. 2 illustrates an optical raster-scanning apparatus in accordancewith another embodiment of the invention.

FIG. 3 illustrates an optical raster-scanning apparatus in accordancewith still another embodiment of the invention.

FIG. 4 is a perspective view of a fast mirror for use in accordance withan embodiment of the invention.

FIG. 5 is a top view of a spring utilized in accordance with anembodiment of the invention.

FIG. 6 is a side view of the spring of FIG. 5.

FIG. 7 is a perspective view of a slow mirror for use in accordance withan embodiment of the invention.

FIG. 8 is an enlarged perspective view of a portion of the slow mirrorof FIG. 7.

FIG. 9 illustrates the frequency response of a fast mirror constructedin accordance with an embodiment of the invention.

FIG. 10 illustrates the frequency response of a slow mirror constructedin accordance with an embodiment of the invention.

FIG. 11 illustrates far-field optical effects of a curved mirror; thisinformation is used in accordance with the invention to compensate formirror curvature.

FIG. 12 illustrates the aperture effect of a mirror in the far-field.

FIG. 13 illustrates the effect of mirror deformation due to comb driveactuation.

Like reference numerals refer to corresponding parts throughout thedrawings.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a simplified representation of an optical raster scanningsystem 20 constructed in accordance with an embodiment of the invention.The system 20 processes a laser beam 22 with a first mirror 30,implemented as a micromechanical device. The first mirror 30 may be a“fast mirror”, as described below, which pivots about a first axis ofrotation 26, causing first rotational motion, as shown with arrow 28. Asdescribed below, the first rotational motion is achieved by pushing orpulling the bottom edge of the mirror 30.

FIG. 1 also illustrates a second mirror 24, which is also implemented asa micromechanical device. The second mirror 24 may be a “slow mirror”,as described below, which pivots about a second axis of rotation 32,causing second rotational motion, as shown with arrow 34. As describedbelow, the second rotational motion is achieved by pushing or pullingthe left and right sides of the mirror 24. By controlling the motion ofthe slow mirror 24 and the fast mirror 30, the laser beam 22 isprojected onto a screen 36 to establish a predetermined pattern, as willbe discussed further below.

FIG. 2 is a more detailed depiction of an optical raster scanning system20 in accordance with an embodiment of the invention. The system 20 ofFIG. 2 has its mirrors 24 and 30 fabricated on a single semiconductorsubstrate 38. A laser 40 generates a laser beam 22, which passes throughan acousto-optic modulator 42. The laser beam 22 is subsequentlydirected through a spatial filter 44 and through a mechanical shutter46. Thereafter, in accordance with a feature of the invention, the laserbeam 22 is processed by mirror curvature compensation optics 48. Theoptic assembly 48 operates to compensate for mirror curvature featuresthat would otherwise degrade optical performance, as discussed in detailbelow. The laser beam 22 is then controlled by the first mirror 30 andthe second mirror 24, with the laser beam 22 output being directed by anoutput mirror 50. Output optics 52 may process the laser beam 22 beforeit is applied to a camera 54 or screen.

The system of FIG. 3 corresponds to the system of FIG. 2 with twoexceptions. First, in the system of FIG. 3, the mirrors 24 and 30 arenot formed on a single substrate, instead they are individuallyfabricated. Second, imaging optics 60 are used between the first mirror30 and the second mirror 24.

The micro-mirrors 24 and 30 are synchronized with a modulated lightsource. Modulation of the light source is used to display informationwith the raster-scanner. Switching the light on-and-off defines thepixels in the display. Grey-scale images can be generated with the useof analog or digital modulation of the light source. Laser diodes andlight-emitting diodes are suitable for this application. Instead of aprojection device 54, light from the micro-mirror display system can beprojected directly on to the retina of the user. Projection on to theretina eliminates the need for a display screen in a head-mounteddisplay. Such an embodiment reduces the weight and cost of the system.

FIG. 4 illustrates a fast mirror 30 constructed in accordance with anembodiment of the invention. The mirror 30 is positioned within a mirrorframe 62. Torsional bars 64A, 64B connect the mirror 30 to the mirrorframe 62. The torsional bars 64 operate in the manner described in thepreviously referenced '297 patent. FIG. 4 further illustrates a mirrorframe lift 66 and a mirror lifter 68. These devices may be fabricatedand otherwise operate in accordance with prior art techniques.

The mirror 30 of FIG. 4 has an associated comb drive 70, which iscontrolled by electrodes 71A, 71B, and 71C. A comb drive central beam 72is driven by the comb drive 70 in a controlled manner. The motion fromthe comb drive central beam 72 is transferred to a mirror slider 73,which pushes or pulls the mirror 30. More particularly, it pushes orpulls the bottom of the mirror 30 to rotate the reflected laser beam.The features discussed in connection with FIG. 4 are consistent withthose described in the '297 patent, with the following exception. Inaccordance with the invention, the comb drive central beam 72 isattached to micromechanical springs 74A and 74B. The springs 74 operateto improve the controlled motion of the mirror 30. In the embodiment ofFIG. 4, the springs 74 are axially aligned with the comb drive centralbeam 72. This configuration has been particularly successful inenhancing the range of motion for the fast mirror 30.

FIG. 5 is a top view of a spring 74 utilized in accordance with anembodiment of the invention. The spring 74 is attached to the comb drivecentral beam 72. The spring 74 includes two interior beams 82A and 82B,two exterior beams 82C, and 82D, and connecting bars 80A and 80B. Beams82A and 82B are attached to an anchor 84.

FIG. 6 is a side view of the spring 74 taken along the line 6—6 of FIG.5. As shown in FIG. 6, the anchor 84 operates to suspend the spring 74over its substrate 86. In particular, FIG. 6 illustrates that beam 82Bis attached to the anchor 84, holding the beam 82B and the remainingportion of the spring above the substrate 86.

Back and forth motion, as illustrated by arrow 90 in FIG. 5, imparted bythe comb drive central beam 72 from the comb drive 70 causes the beams82 to flex in a controlled manner to improve the resultant motionimparted to the mirror 30.

FIG. 7 illustrates a slow mirror 24 positioned on a substrate 90. Theslow mirror 24 has torsion bars 92A and 92B respectively positioned atthe top and bottom of the mirror 24. A mirror frame 94 supports themirror 24, via the torsion bars 92A and 92B. A mirror frame lift 96 andmirror lifter 98 position the mirror 24 over the substrate 90.

FIG. 7 also illustrates individual comb drives 100A and 100B. Each combdrive 100A and 100B respectively controls an individual comb drivecentral beam 102A and 102B. Each comb drive central beam 102A/102B isattached to a mirror slider. Each mirror slider comprises a firsttransverse member (e.g., 105A), which is transverse to its linked combdrive central beam (e.g., 102A), an aligned member (e.g., 108), which isaligned or parallel with its associated comb drive central beam (e.g.,102A), and a second transverse member (e.g., 110A). The secondtransverse members 110A and 110B are respectively connected to mirrorflanges 112A and 112B.

The motion of the slow mirror 24 is controlled by springs 114A and 114B,of the type described in connection with FIGS. 4-6. FIG. 7 illustratesthat the spring 114A has deflected beams (e.g., 116). The orientation ofthe deflected beams indicates that the mirror 24 is being pulled atflange 112A (left side of the mirror out of the page) and pushed atflange 112B (right side of the mirror into the page).

As in the case of the fast mirror 30, the motion of the slow mirror 24is controlled by springs. That is, the springs 114 improve the motion ofthe mirror slider components 108, 105, and 110, which improves themotion imparted to the mirror flanges 112. The configuration of FIG. 7has symmetric actuation imparted by the comb drives 100 to produceimproved mirror motion.

FIG. 8 is an enlarged view of the bottom portion of the slow mirror 24.The figure illustrates the torsion bar 92B. The torsion bar 92B may beconnected to a conventional pin and staple hinge 130.

FIG. 8 also illustrates the mirror flange 112A, which includes a boxframe 122 at its terminal end. The second transverse member 110 of themirror slider includes a T-shaped termination member 124, which ispositioned over the bottom link of the box frame 122. The T-shapedtermination member 124 insures that the second transverse member 110 andthe mirror flange 112 stay assembled. A similar linkage mechanism isused between the fast mirror 30 and its slider 73. Note that the mirrorslider components 105, 108, and 110 are suspended over the substrate 90,allowing controlled motion.

FIG. 8 also illustrates a portion of each individual comb drive 100A and100B. Comb drive segment 131 of comb drive 100B is electricallyconnected to comb drive segment 132 of comb drive 100A. Similarly, combdrive segment 134 of comb drive 100B is electrically connected to combdrive segment 133 of comb drive 100A. If a voltage is applied to combdrive segments 133 and 134, the mirror slider pushes the mirror flange112A into the plane of the page, while the opposite mirror slider pullsthe opposite mirror flange out of the plane of the page, resulting in aclock-wise motion.

The physical components of the apparatus of the invention have now beendescribed. Attention presently turns to a more detailed discussed ofattributes associated with various physical implementations of thedevice. A detailed discussion of the operation of the device will alsofollow. In particular, the following description will addressimprovements in the control signals used in connection with theapparatus and techniques to improve the optical output of the apparatusby compensating for mirror shape anomalies.

Standard MEM processing techniques may be used to fabricate the mirrorsand springs of the invention. In one embodiment of the invention, twofree-standing polysilicon layers are used to create the mirrors (24,30), comb-drives (70, 100) and tilt-up frames (66, 96). The devices maybe fabricated with the Multi-User Microelectromechanical SystemsProcesses (MUMPs) described by K. W. Markus, et al., in “MEMSInfrastructure: The Multi-User MEMS Processes (MUMPs)”, Proc. SPIE, Vol.2639 (Micromachining and Microfabrication Process Technology, Austin,Tex. USA, 23-24, Oct. 5, 1995), p. 54-63. Similarly, the processingtechniques described in the previously referenced '297 patent may beutilized. After fabrication, the devices may be released in a 49%Hydroflouric (HF) acid solution and dried in a supercritical CarbonDioxide (CO₂) chamber. After release and drying, the chips may becovered with 50 nm of aluminum by blanket evaporation to enhance mirrorreflectivity. Overhanging polysilicon structures are preferably used toavoid electrical shorts caused by metal deposition. This design featurewas tested successfully on the single-chip scanner.

The mirrors (24, 30) and torsion beams (64, 92) have been implementedwith 1.5 μm-thick polysilicon. The tilt-up frames, comb-drives andfolded springs have been implemented with 3.5 μm-thick polysilicon. Thetilt-up frames are used to raise the mirrors out-of-plane and hold themsecurely. The frames are connected to the mirrors by torsional hingesand to the chip surface by pin-and-staple hinges, as illustrated inFIGS. 4 and 7. The frames and mirrors may have 3 μm-diameter etch holesspaced on a 30 μm grid for fast release in HF. Each mirror, originallyfabricated flat on the chip surface, may be assembled using a probe on amicropositioner. The probe is used to push forward the lifters 68, 98which are connected to the back of the frames 62, 94. The mechanicalstability of the scanning mirrors can be improved by fixing the framejoints with epoxy.

As previously discussed, the mirrors are actuated by comb-drives thatare connected to the mirrors through hinges near the chip surface. Thecomb-drives move in the plane of the chip. The folded springs (74, 114)provide the majority of the stiffness for the actuator-mirror system.All comb-drives used to actuate the mirrors can be operatedbi-directionally, i.e. two sets of comb teeth are used, one set pullingin the opposite direction of the other. At resonance, a mirror need onlybe driven in one direction, and the inertia of the system will cause itto oscillate nearly symmetrically about its equilibrium point. If amirror is operated below its resonant frequency, it is must be drivenbi-directionally to achieve maximum deflection.

As previously illustrated, the fast mirror 30 rotates about an axisparallel to the chip surface, and the slow mirror 24 rotates about anaxis perpendicular to the surface. The fast mirror 30 may be implementedwith a 65-by-500 μm rectangle flanked by two 500 μm-diameterhalf-circles, making the mirror nearly circular. In one embodiment, itrotates about its long (565 μm) axis, and has a resonant frequency of4.68 KHz (FIG. 4). Fast-mirror frequency-response curves were collectedfrom devices on several chips. Each mirror had a slightly differentresonant frequency, ranging from 4.54 KHz to 4.68 KHz.

All fast mirrors were driven at 4.6 KHz when used to generate thehorizontal component of a raster-scan. The device characterized in FIG.9 is from a single-chip display. The fast-mirror torsional hinges 64 maybe 50 μm×3 μm×1.5 μm, and the folded spring 74 may be 299 μm×3 μm×3.5μm, supporting opposing banks of 66 comb teeth, each 40 μm×3 μm×3.5 μm.The measured optical scan angle of the fast mirror is 15 degrees whenoperated at resonance, driven with a 36.1 V_(rms) sine wave and zero DCoffset. The slow mirror 24 may have the same shape as the fast mirrorbut may be elongated along its axis of rotation by the insertion of a253-by-565 μm rectangle to collect the light from the fast-mirror scan.The slow mirror 24 may be actuated symmetrically by two banks ofcomb-drives (100A, 100B), each driven with a triangular voltage waveformat 60 V_(pp) and zero DC offset. Driving the opposing comb-drives at 90degrees out-of-phase results in a net triangular-force waveform. Using atriangular-shaped waveform instead of a sinusoidal driving signalincreases the linear region of the slow-mirror scan.

The comb drives 100A, 100B for the frame-refresh (slow) mirror 24 ofFIG. 7 are used to produce a push-pull force on the frame-refresh mirror24. The frame-refresh mirror 24 must be driven in both directionsbecause it is operating below its resonant frequency. It is advantageousfor the mirror angle versus time to follow a triangular waveformcentered about zero. By making a fast reversal of the scan direction ateach edge of the frame scan (at the peak or valley of a triangularwaveform), and holding a constant velocity over the majority of theframe, fast-scan lines can be easily projected with uniform spacing.Correction for non-linear velocity changes are not necessary.

The opposing comb drives 100A, 100B allow the use of piecewise linear,symmetric triangle waves to achieve a triangular force waveform formirror actuation. If just one comb drive were used, the netelectrostatic force would be proportional to the square of the appliedvoltage. If a triangular waveform were applied to a single comb drive,the resulting force would not be piecewise linear. A triangular voltagewaveform applied to a mirror with the opposing comb drive design yieldsa net electrostatic force that is proportional to the input voltage (andphase-shifted). The optical modulation for the display need not bemodified to correct for non-linear motion of the mirror.

The slow-mirror folded springs 114 may be 600 μm×3 μm×3.5 μm. The combtooth design is the same as that found on the fast mirror, except 132teeth are available to drive the mirror in each direction. The slowmirror deflects the optical beam through 15 degrees on an axisorthogonal to the fast mirror and has a resonant frequency of 1.14 KHz,as illustrated in FIG. 10.

The slow mirror 24 moves at a sub-harmonic frequency of the fast mirror30. This simplifies the driving electronics for the optical modulator.There are an integer number of line-scan cycles in the image refreshmirror cycle.

The resolution of a raster-display is determined by bothmechanical-system issues and the optical quality of the mirror surfaces.The resonant frequency of the fast mirror limits the display resolutionby restricting the number of lines that can be canned during the imagerefresh period. In visual display systems, ergonomics must be consideredwhen determining the image refresh rate. Factors that affect flickerperception include the location of the image in the visual field, theaverage luminance of the display, and direction of the raster scan. Ahigh-quality scanning display should require an image refresh rate ofabout 100 Hz. Raster-scan images described herein make use of theleft-to-right and top-to-bottom portions of the fast and slow mirrorscans, respectively. Using the other half-cycle of the fast andslow-mirror scans boosts the mechanically-limited resolution by a factorof four.

The optical resolution is a function of the maximum optical scan angledivided by the angular divergence of the reflected laser beam, asdescribed below. Curvature of the mirror surface increases thedivergence angle of the reflected beam. Mirror curvature caused byactuation forces or stress gradients inherent in the fabrication processwill therefore severely degrade the scan resolution if left uncorrected.

The laser 40 of FIGS. 2 and 3 may be a 5 μW, 633 μm Helium-Neon (HeNe)laser source. Unlike spatially incoherent sources, nearly all of alaser's optical power can be focused onto the surface of amicro-scanning mirror, and eventually to the display screen 36 (FIG. 1).This simplifies the transfer of high-optical power density throughmicro-optical systems. In addition, optical analysis is simplified bythe narrow spectral and uniform phase characteristics of the laser. Thefollowing discussion assumes that the light source is monochromatic andspatially coherent with a transverse Gaussian distribution.

Within the Gaussian beam propagation model, the best resolution for anoptical scanner is obtained by positioning the waist of the incidentoptical beam at the surface of the micromirror and the image plane inthe far-field. A number of different geometries will achieve the sameresolution as this configuration, but none are likely to improveperformance. The standard rule of thumb for analog (scanning) cathoderay tube designs is that neighboring pixels should be separated by theFull Width at Half Maximum (FWHM) of their intensity. Given thiscriterion, the number of resolvable spots for a one-dimensional scanneris given by: $\begin{matrix}{N = \frac{{\alpha\pi\omega}_{m}}{1.178\lambda}} & \left( {{Equation}\quad I} \right)\end{matrix}$

where α is the optical scan angle, ω_(m) is the radius of the opticalbeam waist on the mirror (in this discussion, optical beam radius alwaysrefers to the radius of the laser beam at its 1/e² intensity value), andλ is the optical wavelength. To improve the resolution, it is necessaryto increase the product αω_(m). Mirrors that accept a large optical beamand rotate through large angles are desired.

Equation I represents an ideal scanning mirror that is perfectly flatand of infinite extent. Curvature and imperfections of the opticalsurface, as well as the finite size of a real mirror, will reduce theresolution. Stress-gradient-induced mirror curvature is dominant amongthese. In the disclosed two-mirror display system, mirror curvature willtypically cause an increase in the area of the far-field optical beam bya factor of more than 1000 if left uncorrected. By approximating thecurved-mirror profile as parabolic, one can calculate the increase inthe far-field beam size and the proportional reduction in resolution.This may be expressed as the ratio M of the actual optical beam radiusto the theoretical beam radius for an ideal, flat mirror of infiniteextent $\begin{matrix}{M = {\frac{1}{\left| f \middle| \lambda \right.}\sqrt{({f\lambda})^{2} \cdot \left( {\pi\omega}_{m}^{2} \right)^{2}}}} & \left( {{Equation}\quad {II}} \right)\end{matrix}$

where ƒ is the focal length of the mirror and ω_(m) is the radius of theincident optical beam waist on the mirror.

To optically compensate for the curvature of a micromirror, its radiusof curvature, or equivalently, the focal length of the mirror, must befound. To do this, the far-field optical beam radius is measured forseveral laser beam waist sizes on the mirror. Dividing the measuredfar-field optical beam radius by the theoretical far-field optical beamradius of a perfectly flat, infinitely large mirror yields the value ofM. Typical examples of experimentally determined values of M forscanners of the invention are plotted in FIG. 11. Equation II is fittedto these points with ƒ as a fitting parameter. Equation II is, strictlyspeaking, only valid for a mirror of infinite extent, but may be used tofit data for the following reasons. First, for small incidentbeam-waist-radii less than three times the mirror radius, there iseffectively no diffraction off the mirror edges. Second, larger incidentoptical beams are greatly expanded by the mirror curvature in thefar-field, causing the relative influence of the aperture effect to besmall.

Testing with polysilicon mirrors indicates that resolution loss due tocurvature is small for an incident beam waist less than 50 μm. EquationI, however, shows that larger beam radii, and thus larger mirror sizes,are desired to increase resolution. Increasing the radius of the laserbeam on the mirror causes an increased sensitivity to mirror curvature.The mirror characterized in FIG. 11 has an edge-to-center bow ofapproximately 1.2 μum, which is enough to cause an increase in thefar-field optical beam area by a factor of 506 when the mirror is filledwith a 250 μm-radius waist. Stress gradients in the polysilicon,inherent to the fabrication process, are the suspected cause ofcurvature in the mirror. While it may be difficult to flatten the mirrorby entirely eliminating stress gradients from the polysilicon, anoptical correction is achieved in accordance with the invention.

Once the focal length is known, the mirror curvature can be opticallycanceled by appropriately forming the phase front of the incidentoptical beam. Using the Gaussian beam propagation model, a two orthree-lens system can be designed to pre-form the laser beam such thatthe waist of the reflected beam is at the surface of the second mirrorin a two-mirror system. Orthogonal axes on each mirror can beindependently optimized with cylindrical optics. Curvature is thedominant factor in reducing resolution. By correcting for curvature in atwo-mirror system, the radius of the optical beam in the image plane isreduced by a factor typically between 30 and 40. This brings themeasured far-field optical beam size to within 12% of its diffractionlimit (including the aperture effect, see below) simultaneously on bothaxes of a single-chip scanner.

Once the mirror curvature is optically compensated in accordance withthe invention, the aperture effect of the mirror becomes significant indetermining the diffraction-limited far-field optical beam size.Truncation of the Gaussian laser beam at the mirror broadens thefar-field intensity distribution and causes side lobes to appear aboutthe central intensity maximum, as illustrated in FIG. 12. The relativepower in the central and side-lobes is dependent upon the ratio of theincident optical beam radius to the mirror radius. As stated above, ifthe radius of the mirror is at least three times the radius of theoptical beam, the aperture effect of the mirror becomes negligible.Increasing the radius of the incident optical beam reduces the centrallobe width of the diffraction patterns. A larger incident beam radiusalso increases the power in the side-lobes, which is undesirable fordisplay applications. In addition, reflection off of the tilt-up framesurrounding the mirror increases with incident optical beam size,causing artifacts in the raster-scanned image. Taking these factors intoconsideration, a 250 μm-incident beam radius may be chosen, roughlyequivalent to the fast mirror size. For this case, minimal reflectionoff of the frame is observed, and the power in the side lobes is low.The central lobe, however, expands by about 49% compared to anun-apertured beam, as demonstrated in FIG. 12, and this expansion leadsto a proportional reduction of the number of resolvable spots comparedto the infinite-mirror case (equation I).

Actuation forces on the mirrors will also influence the resolution. Theactuators disclosed herein are connected directly to the bottom edges ofthe mirrors through hinges. The comb-drives induce a torque about themirrors' torsional hinges, with the mirror surface acting as the momentarm. The applied force at the edge of the mirror causes bending of theoptical surface that varies with the rotational position of the mirror.FIG. 13 documents the effect of mirror bending on the far-field opticalbeam size. The optical beam size at zero deflection is 400 μm, close tothe 361 μm-predicted diffraction-limit for a 250 μm beam on a 250 μmmirror and a 30 cm-focal-length output lens. Through the entire range ofactuation shown in FIG. 13, the difference between the optical beamradii on perpendicular axes in the far-field remained less than 15%,indicating bending along both axes of the mirror surface.

Connecting the comb-drives to an independent lever arm that is attachedto the mirror near the torsional hinges will remedy the problem ofcurvature induced by static actuation forces.

Inertial and dynamic forces can also play a role in bending the mirrorsurface. Preliminary data suggest that dynamic curvature of the fastmirror has a measurable influence on the far-field beam size when thescanner is operated at resonance.

The preceding mechanical and optical analyses were used in the designand testing of individual micromachined scanners. The two-mirrorraster-scanner design relies on information collected from individualmirrors. The following discussion focuses on the results fromsingle-chip and dual-chip raster scanners.

In the single-chip design, the fast and slow mirrors are positionedopposite each other, separated by an optical path length of 936 μm. Onemethod of optical correction for the mirror curvatures requires that theincident optical beam form a virtual waist behind the fast mirror. Thefast mirror is tilted back approximately 3 degrees from theperpendicular, allowing the converging incident laser beam to reach themirror without grazing the chip surface. The slow mirror is normal tothe chip surface. The stationary output mirror accepts light from theslow mirror and re-directs it through the output optics to the displayscreen or camera.

A 5.02 cm-focal-length lens, followed by a cylindrical concave lens withfocal length -833.3 cm and a 10 cm-focal-length lens correct for thecombined curvature of the two-mirror system. The output mirror, made ofsingle-crystal silicon, has negligible curvature. The optical surface ofthe output mirror must be within approximately 50 μm of the chip surfaceto capture the full raster scan, and the top of the mirror must tiltaway from the slow mirror to direct the light off-chip. To produce asharp edge at the base of the mirror, the silicon was etched in a KOHbath along a crystalline plane at 54.7 degrees with respect to thepolished mirror surface. A micropositioner orients and holds the outputmirror in place. The output optics consist of a 10 cm-focal-length lensand additional optics used to photograph the scan. Due to the geometryof the camera, two 30 cm-focal-length lenses in an 4-f configurationwere needed to transfer the image, found at the back focal plane of the10 cm lens, into the camera. After exiting the second 30 cm-focal-lengthlens, the light falls directly onto the film. Direct imaging of thedisplay onto film eliminates speckle, commonly found in laser projectionsystems. Speckle is caused by optical interference in the lightscattered from a projection screen due to roughness of the screensurface.

To increase the rigidity of the tilt-up frames, all stationary hingejoints are preferably epoxied, with the exception of two joints at thebase of the slow mirror frame. Epoxy was not applied to these stationaryhinges because the adhesive could potentially spread to nearby actuatormembers, causing them to freeze in position.

An acousto-optic modulator in the beam path adjacent to the laser source(element 42 in FIGS. 2 and 3) switches the light on-and-off with asignal that is synchronized to the mirror driving voltages. Theacousto-optic modulator turns off the light in a narrow region (about 7%of the display width) at each edge of the horizontal scan. Thisnon-linear turnaround region of the fast-mirror is not used for imagedisplay. A mechanical shutter 46 selects a half-cycle of the slow mirrorto expose the film. The corrected optical beam size in the center of theimage plane was within 12% of the theoretical diffraction-limitedprediction. The smallest pixel size is at the center of the display,with no voltage applied to the actuators. If the display were filledwith pixels of this size, its resolution would be 176 by 176. Accountingfor the turn-around region on the horizontal scan, the resolution is 151by 176. However, the pixel size varies according to mirror angle.

The highest-resolution region in the image plane is a rectangle runningthe full height of the display and covering about 25% of the horizontalscan width. In this portion of the display, there is little deviation ofthe optical beam size from its minimum. Outside of this area, the scanlines become blurred. At the extreme edges of the display, the far-fieldbeam size expands by roughly a factor of 2.5. By linear approximation,the laser beam expands in size by an average factor of 1.75 over 75% ofthe display. The horizontal display resolution can be approximated basedon average pixel size to be 0.86*176*(0.25+0.75/1.75)=102 pixels. Thisaverage pixel size is used to define the horizontal line spacing becausethe optical beam is essentially circularly symmetric. Therefore, thevertical resolution based on average pixel size is approximately176*(0.25+0.75/1.75)=119, because the fast and slow mirrors rotatethrough the same angle. There is effectively no resolution loss toturn-around regions in the slow-mirror scan because it is driven by atriangular waveform.

Several raster-scanned images were photographed to demonstrate thedisplay system. Dynamic effects, such as jitter and wobble, degrade theimage quality. Jitter in the slow mirror causes bright horizontal lines,resulting from overlapping line scans. Three effects play a role inexpansion of the far-field optical beam size at the end of the fastmirror scan line: static mirror deformation, dynamic mirror deformation,and wobble of the fast mirror. Wobble amplitude in the single-chipdesign appears to be less than the average pixel width. Sub-harmonicwobble was found in the two-chip raster-scanner, which is discussedbelow.

A second optical raster-scanning system was tested independently of thesingle-chip scanner. The two-chip raster-scanner makes use of two fastmirrors oriented with orthogonal scan axes, as shown in FIG. 3. One ofthe fast mirrors performs the same function as the slow mirror in thesingle-chip design. In this embodiment, none of the tilt-up frames wereepoxied. The fast and slow-moving mirrors were operated at 5.3 and 5.7degrees of optical deflection, respectively. Both mirror frames weretilted back with an angle of approximately 7 degrees from theperpendicular. The curvature-correction optics described in the previoussection are used with the exception of the cylindrical lens. An opticalassembly 60 with two 6.29 cm-focal-length lenses in a 4-f configurationis inserted between the mirrors to image the fast mirror onto theslow-moving mirror. These lenses could also be used to correct formirror curvature. The output optics consists of a 30 cm-focal-lengthlens. The camera is positioned at the back-focal-plane of the outputlens. The corrected far-field optical beam size in the image plane is17% larger than the predicted diffraction limit. Compared to thesingle-chip design, a proportionally smaller region of the image isaffected by curvature due to actuation because the scan angle issmaller. The resolution based on average pixel size is estimated to be61 by 65 pixels.

Jitter of the slow-moving mirror in the two-chip system is lessprominent than in the single-chip display. The basic mechanical designof the fast mirror, when used as a slow-moving mirror in the two-chipdisplay, may have superior jitter characteristics over the slow mirrordesign in the single-chip display. The fast-mirror wobble amplitude inthe two-chip display, however, is significantly greater than thecorresponding wobble amplitude found in the single-chip design. This maybe due to more motion of the supporting frames because they were notepoxied in place. The wobble amplitude is greater than the horizontalline separation and the wobble frequency is lower than the rotationalfrequency of the fast mirror. When the system is operating as a display,the acousto-optic modulator selects the upper half-cycle of eachline-scan, selectively switching the light off as the mirror wobbles.Mirror wobble in the two-chip system also interleaves the scan lines,causing the horizontal lines from top-to-bottom to be drawn out ofsequence. To display the raster-image data in the correct sequence,every-other line-scan half-cycle was selected by the acousto-opticmodulator. To maintain proper line spacing in this situation, theslow-scanning mirror frequency must be reduced by half.

In sum, an improved surface-micromachined raster-scanning display hasbeen disclosed. The apparatus has been implemented with a resolution of151 by 176 pixels, and an average resolution of 102 by 119 pixels in asingle-chip system. The tilt-up polysilicon mirror design allows forlarge mirror size and deflection, both shown to be necessary forhigh-resolution displays. Mirror curvature was found to be the primaryfactor that reduces resolution in micromachined scanners. The mirrorcurvature was characterized by measuring the far-field intensitydistributions for a series of incident optical beam sizes and fittingthe data to a theoretical curve. Information gathered from thistechnique determines the configuration of curvature-correcting opticsthat pre-form the optical beam incident on the scanners. This methodsuccessfully reduced the laser beam radius in the image plane of thesingle-chip raster scanner by more than an order of magnitude, bringingit to within 12% of the theoretically-predicted diffraction limit.

Once the static mirror curvature was corrected, the factors limitingresolution and image quality were actuation-induced bending, jitter andwobble of the scanning mirrors. Modifying the fast mirror design byremoving the direct connection of the comb-drive to the bottom of themirror is expected to increase the resolution of the display.Deformation of the mirror can be avoided by connecting the comb-drive tothe mirror through separate polysilicon beams that attach to the edgesof the mirror near its rotational axis.

To reach VGA resolution, the mirrors must increase in size andtilt-angle, and the resonant frequency of the fast mirror should beboosted. Maximizing the mechanical force output of the comb-driveactuators will be required to reach a sufficiently high resonantfrequency. It is likely that stiffening of the fast-mirror surface toreduce dynamic bending will also be necessary.

Those skilled in the art will appreciated that the disclosed technologycan be used in light-weight, low-power, and low-cost video displays. Fora flicker-free video display, the slow mirror should operate between30-100 Hz. The video line-scan rate should be between 30-100 kHz. In thedemonstrated single-chip display, one line is drawn for each half-cycleof the fast mirror, and no lines are drawn during half of the low mirrorcycle. If information is displayed during both half-cycles of the fastand low mirrors, the effective line-scan rate (the number of lines drawnduring one slow mirror cycle) increases by a factor of four. A 10 kHzfast-mirror that has already been demonstrated could produce anequivalent line-scan rate of 40 kHz, which is sufficient to displayvideo. The following mechanical enhancements will improve systemperformance: increasing rotational angle and size of the mirror enableshigher resolution displays, increasing the stiffness of the mirrorsprings increases the line-scan rate, and increasing the mirrorstiffness ensures uniform pixel size across the display.

Those skilled in the art will appreciate that a variety of techniquesmay be used to measure mirror curvature. A mirror may be placed in adevice designed to measure the mirror curvature. The far-fieldcharacteristics of an optical beam reflected off of a micro-mirror canbe used to compute the mirror curvature. The instruments used to measurethe far-field optical beam size may be placed anywhere in the far-field(this can be advantageous) at a known distance from the mirror, and onlyone measurement may be required. From these measurements, the mirrorcurvature can be theoretically extracted and used to design correctiveoptics. The corrective optics may be placed before, between, or afterthe mirrors. In some cases it may be advantageous to place lenses in twoor all three locations. In the case of a micro-display system, it may beadvantageous to place all of the optics after the mirror system tominimize the number of micro-lenses that need to be mounted on the chip.

It is not necessary to remove a micro-mirror from the display system tomeasure micro-mirror curvature. Corrective optics can be optimized forthe curvature of an individual mirror by adjusting lens positions oradjusting the placement of the projection screen in the display system,using the display system laser as the measurement beam. This processfinds the mirror curvature and tunes the corrective optics at the sametime, potentially simplifying the process of building a working display.

Placement of bulk mirror-curvature correction optics that lie externalto the microscopic system may be used in manufacturing micro-displays.In such a case, the light source and mirrors are assembled on asubstrate and are incorporated into a package, without the need tocustomize the optics in the package. Mirror curvature correction isperformed later with a macroscopic lens. Mirror curvature can becorrected by appropriate selection of the output optics, optimumplacement of the display screen, or a combination of the two.

There are numerous causes of mirror curvature, includingstress-gradients, thermal expansion and contraction, static, dynamic,and inertial forces. A system can be engineered to cancel the combinedeffect of mirror curvature in both mirrors without inclusion of externalcurvature-correcting optics. A convex mirror immediately following aconcave mirror with the same absolute radius of curvature can be used tocancel the effect of mirror curvature. Similarly, a concave mirrorfollowed by a convex mirror with the same absolute radius of curvaturecancels the curvature effect.

In micromachined systems, curvature due to stress-gradients is oftenuniform over the small region of the substrate on which the display isfabricated. By fabricating one mirror with its optical surface facingdown, and the other mirror with its optical surface facing up (beforeassembly), the mirrors have opposite concavity after release. Afterrelease and assembly, one mirror is convex and the other concave. Thedivergence or convergence that the first mirror induces in the reflectedoptical wavefront is largely canceled after reflection from the secondmirror.

The foregoing description, for purposes of explanation, used specificnomenclature to provide a thorough understanding of the invention.However, it will be apparent to one skilled in the art that the specificdetails are not required in order to practice the invention. In otherinstances, well known circuits and devices are shown in block diagramform in order to avoid unnecessary distraction from the underlyinginvention. Thus, the foregoing descriptions of specific embodiments ofthe present invention are presented for purposes of illustration anddescription. They are not intended to be exhaustive or to limit theinvention to the precise forms disclosed, obviously many modificationsand variations are possible in view of the above teachings. Theembodiments were chosen and described in order to best explain theprinciples of the invention and its practical applications, the therebyenable others skilled in the art to best utilize the invention andvarious embodiments with various modifications as are suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the following claims and their equivalents.

What is claimed is:
 1. A method of operating a micromechanical scanningapparatus, said method comprising the steps of: identifying a radius ofcurvature value for a micromechanical mirror; and modifying a laser beamthat impinges upon said micromechanical mirror so as to compensate forsaid radius of curvature value so as to improve the optical resolutionof said micromechanical scanning apparatus.
 2. The method of claim 1wherein said identifying step includes the steps of: acquiring ameasured far-field optical beam radius for a laser beam reflected fromsaid micromechanical mirror; dividing said measured far-field opticalbeam radius by a theoretical far-field optical beam radius reflectedfrom an ideal mirror to yield a ratio value M; curve fitting ananalytical expression for M to experimental data for M with focal-lengthas a fitting parameter; and multiplying said focal-length of said curvefitting step by two to establish said radius of curvature.
 3. The methodof claim 2 wherein said dividing step includes the step of dividing saidmeasured far-field optical beam radius by a theoretical far-fieldoptical beam radius from a perfectly flat, infinitely large theoreticalmirror to yield said ratio value M.
 4. The method of claim 1 whereinsaid modifying step includes the step of optically modifying said laserbeam to compensate for said radius of curvature.
 5. The method of claim4 wherein said modifying step includes the step of re-shaping the phasefront of said laser beam to compensate for said radius of curvature. 6.The method of claim 1 wherein said modifying step includes the step ofoptically modifying said laser beam within said micromechanical scanningapparatus.
 7. The method of claim 1 wherein said modifying step includesthe step of optically modifying said laser beam outside of saidmicromechanical scanning apparatus.
 8. The method of claim 7 whereinsaid modifying step includes the step of optically modifying said laserbeam with macroscopic lenses.
 9. The method of claim 7 wherein saidmodifying step includes the step of optically modifying said laser beamthrough positioning of a display screen.
 10. The method of claim 7wherein said modifying step includes the step of modifying said laserbeam with a second micromechanical mirror with a radius of curvaturevalue that is opposite said radius of curvature value for saidmicromechanical mirror.
 11. The method of claim 1 further comprising thestep of synchronizing a first micromechanical mirror with a secondmicromechanical mirror with a modulated light source to produce adisplayed image.
 12. The method of claim 11 further comprising the stepof operating said modulated light source to produce grey-scale imageswithin said displayed image.
 13. The method of claim 11 furthercomprising the step of projecting said displayed image onto the retinaof an eye.
 14. The method of claim 11 wherein said secondmicromechanical mirror moves at a sub-harmonic frequency of said firstmicromechanical mirror.